edu.northwestern.at.utils.math.distributions

## Class Normal

• java.lang.Object
• edu.northwestern.at.utils.math.distributions.Normal

• ```public class Normal
extends java.lang.Object```
Normal distribution functions.
• ### Constructor Summary

Constructors
Modifier Constructor and Description
`protected ` `Normal()`
Make class non-instantiable but inheritable.
• ### Method Summary

Methods
Modifier and Type Method and Description
`static double` `normal(double z)`
Compute probability for normal distribution.
`static double` `normalInverse(double p)`
Compute percentage point for normal distribution.
`static double` `normalInverseBad(double p)`
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ### Constructor Detail

• #### Normal

`protected Normal()`
Make class non-instantiable but inheritable.
• ### Method Detail

• #### normal

`public static double normal(double z)`
Compute probability for normal distribution.
Parameters:
`z` - Percentage point of normal distribution.
Returns:
The corresponding probabiity for the Student t distribution.

Uses the relationship between the Normal and Gaussian Error distributions.

• #### normalInverse

```public static double normalInverse(double p)
throws java.lang.IllegalArgumentException```
Compute percentage point for normal distribution.
Parameters:
`p` - Probability value.
Returns:
The corresponding approximate percentage point for the normal distribution.

See Wichura, M. J. (1988) Algorithm AS 241: The Percentage Points of the Normal Distribution. Applied Statistics, 37, 477-484. The result is generally accurate to about 10-12 decimal digits. We improve the result from Wichura's estimate using two iterations of a Taylor series, generally resulting in about 15 decimal digits of accuracy. See Kennedy, W. J. and Gentle, James E. _Statistical Computing_, Marcel Dekker, 1980, pp. 94 for a discussion of the Taylor series improvement.

Throws:
`java.lang.IllegalArgumentException`
`public static double normalInverseBad(double p)`